6.3: Fractions as Percents

Have you ever thought about a statistic in terms of percent? Take a look at this dilemma.

After conducting a survey of middle school students, Justin learned that 19 out of 50 students will attend summer camp. This is his statistic.

What is this statistic as a percent?

This Concept is about writing fractions as percents. You will be able to complete this problem at the end of the Concept.

Guidance

A fraction can be written as a percent if it has a denominator of 100
. Sometimes, you will be given a fraction with a denominator of 100 and sometimes you will have to rewrite the fraction to have denominator of 100 before you write it as a percent.

This fraction is already written with a denominator of 100, so we can just change it to a percent.

What do we do if a fraction does not have a denominator of 100?

This is where your work with
proportions
and equal ratios comes in.
Remember that a proportion is two equal ratios. We can write a proportion for a fraction by creating a second fraction equal to the first that has a denominator of 100. Then we solve the proportion.
It sounds trickier than it is. Let’s look at an example.

Write
as a percent.

To start with, notice that the denominator is not 100. Therefore, we need to create a new fraction equivalent to this one with a denominator of 100.

Wow! Here is a proportion. Next, think back to solving proportions. We can cross multiply to find the value of
.

Now we have a fraction with a denominator of 100. We can write it as a percent.

Our answer is that
is equal to 60%.

What about if we had an improper fraction?

To work with an improper fraction, you have to think about what that means. An improper fraction is greater than 1, so the percent would be greater than 100%
. Sometimes in life we can have numbers that are greater than 100%. Most often they aren’t, but it is important to understand how to work with a percent that is greater than 100.

Write
as a percent.

First, we write a proportion with a denominator of 100.

Next, we cross multiply to find the value of
.

Our answer is 225%.

Did you know that you already know some common fraction equivalents for percents?
Think of 25 cents, 50 cents, and 75 cents.

25 cents means 25 cents out of a dollar, or 25% of a dollar. Since a quarter is 25 cents,
.

50 cents means 50 cents out of a dollar, or 50% of a dollar. Since a half dollar is 50 cents,
.

75 cents means 75 cents out of a dollar, or 75% of a dollar. Since three quarters is 75 cents,
.